Brini, A. orcid.org/0000-0002-3758-827X, Cavalieri, R. and Ross, D. (2019) Crepant resolutions and open strings. Journal für die reine und angewandte Mathematik (Crelles Journal), 2019 (755). pp. 191-245. ISSN 0075-4102
Abstract
In the present paper, we formulate a Crepant Resolution Correspondence for open Gromov–Witten invariants (OCRC) of toric Lagrangian branes inside Calabi–Yau 3-orbifolds by encoding the open theories into sections of Givental’s symplectic vector space. The correspondence can be phrased as the identification of these sections via a linear morphism of Givental spaces. We deduce from this a Bryan–Graber-type statement for disk invariants, which we extend to arbitrary topologies in the Hard Lefschetz case. Motivated by ideas of Iritani, Coates–Corti–Iritani–Tseng and Ruan, we furthermore propose (1) a general form of the morphism entering the OCRC, which arises from a geometric correspondence between equivariant K-groups, and (2) an all-genus version of the OCRC for Hard Lefschetz targets. We provide a complete proof of both statements in the case of minimal resolutions of threefold An-singularities; as a necessary step of the proof we establish the all-genus closed Crepant Resolution Conjecture with descendents in its strongest form for this class of examples. Our methods rely on a new description of the quantum D-modules underlying the equivariant Gromov–Witten theory of this family of targets.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 de Gruyter. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 11 Nov 2019 15:32 |
Last Modified: | 11 Nov 2019 15:32 |
Status: | Published |
Publisher: | Walter de Gruyter GmbH |
Refereed: | Yes |
Identification Number: | 10.1515/crelle-2017-0011 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150353 |